Gauff, whose lead-up to the US Open included hardcourt titles in Washington and Cincinnati, converted six of her seven break points and dropped serve just once during the 67-minute match in Arthur Ashe Stadium where the temperature rose above 90 Fahrenheit (32.2 Celsius).
"It feels great, so happy," Gauff said during her on-court interview. "Last year I lost in the quarter-final stage and I wanted to do better this year.
"I am happy and ready to get back to work for the next one."
Ostapenko entered the match full of confidence having upset world number one Iga Swiatek in the previous round but against Gauff the misfiring Latvian 20th seed could not find her range and delivered an error-filled performance.
Gauff was in control from the start and showcased excellent court coverage while delivering a steady stream of balls deep into the corners en route to capturing the first set in 20 minutes and limiting Ostapenko to seven points.
Former French Open champion Ostapenko, playing in her first US Open quarter-final, finally got on the board with a break to level the second set at 1-1 but Gauff never wavered and broke back for a 2-1 lead with a backhand crosscourt winner.
Ostapenko held serve for the first time 49 minutes into the match but Gauff went up a double break for a 5-2 lead before closing out the encounter on her serve in a game in which she had to come back after falling behind 0-30.
By the time it was over, Ostapenko had 36 unforced errors compared to 14 for Gauff.
With the win, Gauff avenged her round of 16 loss to the Latvian at this year's Australian Open that left the American in tears.
Despite delivering a lopsided win to reach the second semi-final of her career, Gauff said she never felt comfortable on the court against Ostapenko.
"I know the game she plays, she has ability to come back no matter the scoreline, so I was just really trying to get every point, trying to play every ball in," said Gauff.
"It's really tough against her because you can't really be aggressive, so I was trying my best to be aggressive when I could and most of the time I was just trying to get the ball deep."
Up next for Gauff, who is the youngest American to reach the US Open semi-finals since Serena Williams in 2001, will be either Czech 10th seed and French Open finalist Karolina Muchova or Romanian 30th seed Sorana Cirstea.
